Resumen en español

Controlled formation of molecules in the ground state has represented a challenge. Nevertheless, there has been important advances in this direction in molecular physics and chemistry due to its variety of applications, specially for being good candidates for quantum simulators. Photoassociation is a technique developed to achieve this task starting from ultracold gases of atoms and carefully carrying it to a molecular system in the ground state. This technique has been proved to be enhanced via spin-orbit couplings in the system. Due to this, it is important to understand from a relativistic point of view the behavior of molecular systems. In this work we present a numerical approach to the solution of the Dirac equation for the H+ 2 molecule. In the first chapter we show the methodology used to reduce the problem to a generalized eigenvalue problem. In the second chapter we describe the numerical implementation which is finally used to calculate the ground state energy for the system and we discuss on the convergence of the results obtained.